What is the integral of x(3x^2-5)^{9/2} ?

The integral of x(3x^2-5)^{9/2} is 1/33 (3x^2-5)^{11/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(3x^2-5)^{9/2}

\int x (3 x^{2} - 5)^{\frac{9}{2}} d x

\frac{1}{33} (3 x^{2} - 5)^{\frac{11}{2}} + C

Solution steps

\int x (3 x^{2} - 5)^{\frac{9}{2}} d x

Apply u-substitution

: \int \frac{u ^{\frac{9}{2}}}{6} d u

= \int \frac{u ^{\frac{9}{2}}}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int u^{\frac{9}{2}} d u

Apply the Power Rule

: \frac{2}{11} u^{\frac{11}{2}}

= \frac{1}{6} \cdot \frac{2}{11} u^{\frac{11}{2}}

Substitute back

u = 3 x^{2} - 5

= \frac{1}{6} \cdot \frac{2}{11} (3 x^{2} - 5)^{\frac{11}{2}}

Simplify

\frac{1}{6} \cdot \frac{2}{11} (3 x^{2} - 5)^{\frac{11}{2}} : \frac{1}{33} (3 x^{2} - 5)^{\frac{11}{2}}

= \frac{1}{33} (3 x^{2} - 5)^{\frac{11}{2}}

Add a constant to the solution

= \frac{1}{33} (3 x^{2} - 5)^{\frac{11}{2}} + C

\int x^{- 3} x d x

\int e^{x} 1 0^{x} d x

\int \frac{2 x ^{3}}{x ^{4} + 1} d x

\int \frac{2}{100 - t} d t

\int \frac{- cos ( x )}{sin ^{5} ( x )} d x

What is the integral of x(3x^2-5)^{9/2} ?
The integral of x(3x^2-5)^{9/2} is 1/33 (3x^2-5)^{11/2}+C